If the Earth's magnetic field disappeared, more particles from the Sun and
from the cosmic radiation would reach the surface. At the moment, many
particles
can reach the surface at the Poles because the field is vertical there so
the particles quite easily make it down along the field lines to the
surface. Near the equator the particles are scattered away from Earth by the
horizontal field lines.

Therefore, if the field disappeared altogether I think conditions would be
like they are now near the poles, all over Earth. There would be plenty of
something like aurora, but aurora depends on field lines for making the
wavy curtains so I guess there would be more of an even glow, in the
absence of a magnetic field. The glow would be very weak, though, because the
magnetic fields are needed to trap the particles to keep the glow going.

The oceans and the atmsophere would not boil away. We know that because the
field does disappear every now and then! The field reverses its polarity
and for a while there is no field, and then it returns with opposite
polarity. This has happened many times - the evidence is frozen in
magnetic fields in rocks that form from the molten state.